Only hours after Congress adopted a bill to avert the “fiscal cliff” of tax increases and spending cuts, lawmakers on Wednesday began to clash over the limit on federal borrowing, inaugurating the next phase of Washington’s permanent fiscal war.

Republicans said they will press their demand that spending be reduced dramatically in exchange for allowing any more U.S. borrowing. But President Obama and top Democrats insisted that their goal of raising the $16.4 trillion federal debt ceiling is non-negotiable.

The government has reached its debt limit — a statutory cap on borrowing — and has about two months to go before it exhausts “extraordinary measures” being used to fund federal operations. Not raising the debt ceiling probably would prompt a default on U.S. government debt and at least a short-term financial crisis.

Senate Minority Leader Mitch McConnell (R-Ky.) on Wednesday called for the Senate to take the lead and address the debt ceiling by early next month with legislation that would significantly trim spending.

“Democrats now have the opportunity — and the responsibility — to join Republicans in a serious effort to reduce Washington’s out-of-control spending,” McConnell said. “That’s a debate the American people want. It’s the debate we’ll have next. And it’s a debate Republicans are ready for.”

House Speaker John A. Boehner (R-Ohio) plans to advance his own measure, “with an attached large package of spending cuts,” aides say. He pledged to do so in a meeting with GOP lawmakers last week.

Boehner has maintained that any increase in the debt ceiling must be offset by an equivalent reduction in federal spending.

The battle over the fiscal cliff ended with many Republicans reluctantly voting to pass the first significant tax increase in 20 years, and they now view the debt limit as a source of leverage that would shift power in Washington back their way.

Obama’s allies say the president is willing to cut more spending as long as Republicans are able to raise more tax revenue from the wealthy. But they insist that he will keep his pledge not to negotiate over the debt ceiling.

“He’s not going to be politically blackmailed with the debt-ceiling threat,” said Rep. Chris Van Hollen (Md.), a friend of the White House and the ranking Democrat on the House Budget Committee.

In the summer of 2011, when the government was running up against the debt ceiling, Obama engaged in months of negotiations with Republicans over raising the limit, bringing the government to the edge of default. Speaking at the White House on Tuesday night before decamping to Hawaii to finish his holiday vacation, he said he would not do so again.

“I will not have another debate with this Congress over whether or not they should pay the bills that they’ve already racked up,” the president said.

Republicans say Obama will have no choice but to negotiate over the debt limit. In an interview Tuesday, McConnell said that is the only way Republicans can force spending cuts necessary to keep the country on sound economic footing.

“Regretfully, the only time in the past that we’ve been able to get this administration to even talk about reducing spending has been when they ask us to raise the debt ceiling,” he said. “What other leverage point do we have to get a reluctant president . . . to talk about the real problem?”

McConnell added that although he would participate in further talks, he did not see a need for additional tax revenue. “We’ve settled the tax question, but we don’t have a revenue problem,” he said.

Although the fiscal cliff deal avoided the immediate threat to the economy, the failure to address the debt ceiling continues to take a toll.

“This debate will re-introduce uncertainty to financial markets and will likely weigh on business and consumer confidence,” economists at Wells Fargo wrote on Wednesday in a report.

The last debt-ceiling imbroglio, in summer 2011, ended with the U.S. credit rating being downgraded.

Obama has proposed giving the president the power to unilaterally raise the debt ceiling unless Congress overrides the action by a two-thirds majority. Treasury Secretary Timothy F. Geithner has argued that the debt ceiling should be eliminated. And on Wednesday, some Democrats said they will pursue legislation to do just that.

“We must ensure that we never have another crisis in which the American economy is held hostage to advance the political demands of the most unreasonable and extremist members of Congress,” said Rep. Jerrold Nadler (N.Y.).

But Rep. Jack Kingston (R-Ga.) said another fight is inevitable, given Republicans’ insistence on slimming the government.

“We all know that, in two months, we’re going to have this same drama unfold again,” he said Wednesday on MSNBC. So to me, it’s very frustrating that, at some point, someone besides conservatives in the House are going to have to say, ‘You know what? We’ve got to get our fiscal situation in order.’ ”

Paul Kane and Rosalind S. Helderman contributed to this report.

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